Drug Diffusion and Nano Excipient Formation Studied by Electrodynamic Methods

Full text

(1)Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 293. Drug Diffusion and Nano Excipient Formation Studied by Electrodynamic Methods ULRIKA BROHEDE. ACTA UNIVERSITATIS UPSALIENSIS UPPSALA 2007. ISSN 1651-6214 ISBN 978-91-554-6864-4 urn:nbn:se:uu:diva-7818.

(2)

(3)

(4)

(5)

(6)

(7)

(8) !

(9) "

(10) " # # $% & ! & & '! !( )!

(11)

(12) *

(13)

(14) +

(15) !( , ! ( #( &&

(16)

(17) -

(18) +

(19) .

(20) / +

(21) " ! ( 0

(22)

(23) (

(24)

(25)

(26)

(27) 1$( #$ ( ( 2/,- 1#34145564737646( -*

(28)

(29) *

(30)

(31) *

(32) ! & !

(33) ! 8

(34) ( )! !

(35) ! &

(36)

(37)

(38) *

(39) ! &

(40) ! &&

(41) 4 * ! &

(42) &

(43) * & !

(44)

(45)

(46) ( &&

(47) & &&

(48) ! *

(49) ( )!

(50) & !

(51) *

(52)

(53) ! 9 ! .

(54) &&

(55)

(56) !

(57)

(58)

(59)

(60) ! .

(61)

(62) & !

(63)

(64)

(65) &( ) 4

(66)

(67) &

(68) *

(69)

(70)

(71) &

(72) ! &&4

(73) ( '

(74) ! *

(75) &

(76)

(77)

(78)

(79)

(80) ! * !

(81)

(82)

(83)

(84) ( . ! 4 *

(85) *& ! &

(86)

(87) ! & &

(88) &

(89) &

(90)

(91) ( .

(92)

(93) *

(94) & ! * 4

(95)

(96) ! 0"/4

(97) ! *

(98) ! !. 4

(99)

(100)

(101)

(102) ! *& !

(103) ! & !

(104) ! &

(105)

(106) ! & !(

(107) ! &&

(108) ! "

(109) # " ! $ %&'" " #()%*+* " : ; , ! # 2//- 75476 2/,- 1#34145564737646

(110) %

(111)

(112) %%% 4#33 <! %==

(113) (;(= >

(114) ?

(115) %

(116)

(117) %%% 4#33@.

(118) till min familj.

(119)

(120) Papers discussed. This thesis is a summary based on the following papers, which are referred to in the text by their Roman numerals. Reprints were made with permis-. sion from the publishers. I. Characterization of the drug release process by investigation of its temperature dependence Ulrika Brohede, Göran Frenning and Maria Strømme Journal of Pharmaceutical Sciences; 2004, 93(7), p:17961803. II. Electrodynamic investigations of ion transport and structural properties in drug containing gels: Dielectric spec troscopy and transient current measurements on Catan ionic Carbopol systems. Ulrika Brohede, Tobias Bramer, Katarina Edsman and Maria Strømme Journal of Physical Chemistry B, 2005, 109, p:15250-15255. III. Percolating ion transport in binary mixtures with high dielectric loss Ulrika Brohede and Maria Strømme Applied Physics Letters, 2006, 88, p:214103(1-3). IV. Finite element analysis of drug release from cylindrical matrix systems Göran Frenning, Ulrika Brohede and Maria Strømme Journal of controlled release, 2005, 107,(2), p: 320-329. V. Percolative drug diffusion from cylindrical matrix systems with unsealed boundaries Ulrika Brohede, Sima Valizadeh, Göran, Frenning and Maria Strømme Journal of Pharmaceutical Sciences, 2007, 96, in press..

(121) VI. A mechanistic study of the synthesis of AMS-n mesoporous structures from in situ conductivity measurements Alfonso E. Garcia-Bennett, Ulrika Brohede, Robert Hodgkins, Niklas Hedin and Maria Strømme Submitted. VII. Sustained Release from Mesoporous Nanoparticles: Evaluation of structural properties associated with controlled release rate Ulrika Brohede, Rambabu Atluri, Alfonso E. Garcia-Bennett and Maria Strømme Submitted. Comments on my contribution to the papers listed above: I prepared all samples and performed all experiments and was primarily responsible for the writing, with the exeptions listed below: I II III IV V VI VII. I did not perform the SEM imaging. I was not involved in the sample preparation. I did not perform the mercury intrusion measurement, but did the analysis. I was only partly involved in the writing process but not in the model development. I did not perform the mercury intrusion measurement, but did the analysis. I did not perform the SEM imaging. I did not perform the: HRTEM imaging, MAS-NMR spectroscopy, DLS measurements or X-ray diffraction analysis. I was only partly involved in the writing process. I did not prepare the mesoporous silica samples and did not perform the TG analysis..

(122) Publications not included in this thesis, but of general interest to the reader: Percolation phenomena in controlled drug release matrices studied by dielectric spectroscopy and the alternating ionic current method. U. Brohede and M Strømme Journal of non-crystalline solids, 2007, in press “The importance of water transport properties for drug diffusion in cellulose” Ulrika Brohede, Martin Nilsson and Maria Strømme Läkemedelsakademins temakonferens i samarbete med Föreningen för Galenisk farmaci och Biofarmaci, en sektion inom apotekarsociteten temakonferens: Styrning av läkemedelstillförsel-aktuell svensk forskning, Göteborg, Sweden 2-3/6 2004 Percolating ion transport in binary mixtures with high dielectric loss: Dry dielectric spectroscopy recordings and wet time-dependent salt release measurements. Ulrika Brohede and Maria Strømme 9th International Conference on Dielectric & Related Phenomena, Poznan, Poland 3-7 September 2006 Enhanced proton diffusion in mesoporous nanostructures Ulrika Brohede, Rambabu Atluri, Alfonso E. Garcia-Bennett, Göran Frenning and Maria Strømme In manuscript.

(123)

(124) Contents. 1. Introduction...............................................................................................11 1.1 A brief history of pharmaceutics ........................................................11 1.2 Material science and pharmaceutics...................................................11 2. Aims of this thesis.....................................................................................14 3. Drug delivery systems...............................................................................15 3.1 Fast drug release from a tablet ...........................................................15 3.2 Delayed drug release ..........................................................................16 3.3 Sustained drug release ........................................................................16 3.3.1 Tablets ........................................................................................16 3.3.2 Gels.............................................................................................17 3.4 Mesoporous Silica ..............................................................................17 4. Transport processes...................................................................................19 4.1 Diffusion.............................................................................................19 4.2 Conduction .........................................................................................20 4.2.1 Einstein relation ..........................................................................21 4.3 Percolation..........................................................................................21 5. Materials and Sample Preparation ............................................................23 5.1 Tablets ................................................................................................23 5.1.1 Excipient material.......................................................................23 5.1.2 Model drugs ................................................................................23 5.1.3 Sample preparation .....................................................................24 5.2 Gels ....................................................................................................25 5.2.1 Polymer.......................................................................................25 5.2.2 Drug ............................................................................................25 5.2.3 Sample preparation .....................................................................25 5.3 AMS-n, mesoporous silica .................................................................27 5.3.1 Material.......................................................................................27 5.3.2 Model Drugs ...............................................................................27 5.3.3 Synthesis .....................................................................................27 6. Experimental Methods ..............................................................................29 6.1 Electrodynamic methods ....................................................................29 6.1.1 Alternating Ionic Current (AIC) measurements .........................29.

(125) 6.1.2 Dielectric Spectroscopy ..............................................................30 6.1.3 Transient Ionic Currents measurements .....................................34 6.2 Pore structure determining methods...................................................35 6.2.1 Gas adsorption ............................................................................36 6.2.2 Hg-porosimetry...........................................................................38 7. Results and Discussion .............................................................................39 7.1 Drug diffusion in MCC tablets...........................................................39 7.1.1 Tablet characterization................................................................39 7.1.2 Drug release ................................................................................40 7.2 Diffusion in EC tablets .......................................................................42 7.2.1 Model calculations......................................................................42 7.2.2 Drug release ................................................................................43 7.2.3 Dielectric spectroscopy...............................................................45 7.3 Structural characterization of gels......................................................50 7.3.1 Dielectric spectroscopy...............................................................50 7.3.2 Transient current measurements .................................................53 7.4 Mesoporous Silica ..............................................................................56 7.4.1 Synthesis .....................................................................................56 7.4.2 Drug release ................................................................................58 Summary of Appended Papers......................................................................61 Acknowledgements.......................................................................................65 Sammanfattning på svenska..........................................................................67.

(126) 1. Introduction. 1.1 A brief history of pharmaceutics During the 13th century, a new profession was established which was specialized in making medicine.1 Until the beginning of the 19th century the drugs were mostly made of dried plants but also some inorganic salts and alkaloids. The word drug actually has its origin in the old German word for dry (droege, today: trocken) which intended the dried plants.1 In the beginning the drugs were still individually produced and the medicine manufacturing was a true hand craft, the spherical pills were made by hand. The compressed dosage form, known as tablets was not known until the end of the 19th century.2 The scientific breakthroughs in the chemistry research area lead to the ability of synthesizing the drugs. One example is the synthesis of acetylsalicylic acid, also known as Aspirin, used in one of the studies in this thesis, that was discovered 1898 by Felix Hoffman.3 It is a synthetic form of filipendula (spirea) ulmaria used in pharmaceutical applications since the 16th century. In the beginning of the 1930s the industry had grown considerably and the doses became standardized.3, 4 In Sweden the first institute of pharmacy was founded in 1864, but it was not incorporated as a part of the university until 1881. The old knowledge of medicine manufacturing finally came to be a separate university subject when the first professor of a pharmacy-related subject was installed in 1950. In 1975, pharmaceutics became a university degree. Since then the field of pharmaceutics has been a constantly growing research area.. 1.2 Material science and pharmaceutics Medicines are drug delivery systems, containing not only the effective substance but a combination of compounds forming a complete system for a safe and controlled drug administration. The drug molecules are surrounded by compounds, called excipients, with different functions, including filling materials, colouring agents, storing promoters, homogenisers, stability en11.

(127) hancers to make a complete delivery system.5 The excipients form the matrix in the drug delivery system and its properties are crucial for the drug administration. The most frequently used drug administration route is the oral, which also is the simplest and most convenient one. Microcrystalline cellulose is the most commonly used excipient material in tablet manufacturing for the oral administration route. It is a non-toxic readily available material made of a rest product from the wood pulp industry. In a wet environment, e.g. in the gastro-intestinal tract, cellulose absorbs the moist whereby it swells and disintegrates and promotes a fast drug release. The water-cellulose interaction plays an important role in the drug delivery process and is of large interest for researchers today.6 One big challenge for pharmacists today is to achieve controlled drug release from tablets.7-9 This can be done by using a non-swelling, nondisintegrating cellulose, e.g., hydrophobic ethyl cellulose. Ethyl cellulose is a modified wood pulp cellulose that, excepting pharmaceutical applications, mostly has been used as a coating material in military applications.10 When no water-cellulose interaction occurs, drug release is driven by a concentration gradient and takes place only in the pore system of the as-synthesised tablet. For other administration systems than tablets, there is also an interest in obtaining a controlled drug release. For instance from a gel that is developed to have a long adhesion time to the eye mucosa, it is of interest to deliver the drug during the entire contact time.11, 12 One way to achieve controlled drug release from gel formulations is to use cationic systems.13, 14 Today, with the new nanotechnology at hand, researchers strive for even better materials for drug delivery usage. The possibility to geometrically design materials and even functionalize the material surface is of large interest. One of the most promising categories of nanoparticles for which an internal ordered structure may be tailored to host differently sized drug molecules as well as to create predetermined release profiles are the amorphous silica-based materials. The main scope for the thesis was to examine the drug diffusion processes both in traditional drug delivery materials, such as microcrystalline and ethyl celluloses and other less commonly used pharmaceutical excipient materials, such as the cationic systems, and an impending nanotype drug delivery material; mesoporous silica. The material characterization, regarding pore structures, of pharmaceutical materials is to a large extent much the same as for materials used in other applications.5 The drug release process is traditionally measured by the standardized USP cage- or paddle method,15 depicted in figure 1. The system under study is placed in a release medium of at least one litre in volume, and the drug is released into the medium. After sufficiently long time a small sample of the medium can be removed and analysed by a spectroscopic or 12.

(128) conductivity-based method to detect the released drug. The drug release condition in the USP method differs from the in-vivo condition, mainly in the sense of liquid amount since for instance the gastro-intestinal tract or in particular the mouth cavity in comparison is a low liquid environment. Furthermore, because of the time interval for sample extraction of the release medium, the drug release is not measured at-time and fast processes that occur during the drug release are not detectable.. Figure 1. The traditional drug release measuring techniques by the USP cage- (left) and paddle- (right) methods.. Many drugs are ionic salts, which makes it possible to measure the drug transport in the material with electrodynamic methods. The techniques, which are frequently used in solid state physics and electrochemistry applications, are based on the motion of charged particles, ions or rotating dipoles in response to an electromagnetic field and offer insight into the nanoscale properties of materials. Such methods can be used to observe the drug release process on shorter time scales and at earlier release stages than traditional pharmaceutical test methods.16, 17 It is also possible to characterize the individual diffusion coefficients in a more complex delivery system, such a gel system, by such methods (Paper II). In this work drug diffusion processes and formation of nano excipients are studied by selected electrodynamic methods, traditional or tailor made, from the physicist’s view angle in order to gain information necessary for the development process of drug delivery systems.. 13.

(129) 2. Aims of this thesis. The general aims of this thesis were to obtain more fundamental information about the drug transport mechanisms in pharmaceutical materials using electrodynamic measuring techniques and also to in-depth study the synthesis process of a promising future pharmaceutical nano excipient material. The specific objectives of the projects were: To investigate ionic transport mechanisms and water-cellulose interactions by studying drug release from microcrystalline cellulose tablets as a function of temperature (Paper I). To analyse ionic diffusion and migration in an inert ethyl cellulose matrix by using percolation theory, to investigate drug release from cylindrical tablets and to evaluate a power-law method for extracting the dc conductivity from ion-conducting system (Paper III, IV, V). To investigate the potential of electrodynamic methods as characterization tools for diffusion and release processes in complex pharmaceutical gel systems (Paper II). To analyse the synthesis process of mesoporous silica nano and micro particles and to evaluate the structural properties associated with model drug release from these (Paper VI, VII).. 14.

(130) 3. Drug delivery systems. Drug delivery systems are relatively complex chemical products designed to release the desired dose of an active pharmaceutical substance at a well defined rate at the desired location in the body. In addition to the active substance, they therefore contain one or more excipient materials.5 The drug delivery process starts as the equilibrium of the system is disturbed and the drug molecules, often ions, are set in motion. The driving forces for molecular motions are in general concentration gradients, electric fields and temperature changes, where the first mentioned is the driving force in drug release processes.18 When ionic drug molecules are forced in motion by an applied electric field the transport mechanisms can be studied in detail by electrodynamic methods. The matrix surrounding the drug molecule controls the release process. In a real system the matrix contains several exipient materials having diverse functionalities.5 In simplified systems, used for the study of drug release processes, the exipients are minimized to as few components as possible and a model drug is often used, mainly depending on the availability and safety of handling. Since drugs often are salts it is convenient to substitute another salt for the real drug. The properties of a model drug decide which one to use. In a study of a system with a readily soluble drug, sodium chloride, known as table salt, can be used a model drug (Paper I and V), or for a system with sparingly soluble drug, acetylsalicylic acid is often used (Paper IV). The ability of a model drug to ionize when released in a solvent is of importance when using electrodynamic measuring techniques to study the release process. Delivery systems may be separated by their release rate into instant-, delayed- and sustained release systems.5. 3.1 Fast drug release from a tablet The vast majority of dosage forms are tablets, for oral administration. The most commonly used excipient material is microcrystalline cellulose (MCC), which provides an instant drug release system. MCC is made by a rest product from the wood pulp industry and is therefore readily available and relatively inexpensive. On a large scale the material is disordered but on sub 15.

(131) micron scale the structure is crystalline. It is electrically insulating and hygroscopic. After administration of a water-absorbing MCC containing tablet the matrix swells and disintegrates which is one step in a sequence of processes, including drug dissolution and diffusion, leading to the drug release. Each of the processes can be rate-limiting steps for the bioavailability.5 Both disintegration and dissolution are highly dependent on the access of liquid; therefore knowledge about water interactions is crucial for the understanding of the drug release process (Paper I).. 3.2 Delayed drug release In many therapeutic situations one would like to delay the drug release from the delivering vehicle. In, e.g., a two-step treatment, it would be convenient to take both doses at the same time in order to increase patient compliance, or when a drug is destroyed in contact with the gastro-intestinal fluids, the drug release needs to be delayed to occur in the small intestine in order to ensure a good bioavailability. This may be achieved by coverage, or coating, of the tablets or filling granules in capsules, which burst and release the drugs in at the right location.. 3.3 Sustained drug release Sustained release means that the release of the drug from the drug releasing system is extended over time. Sustained release systems enable a superior control over the maintenance of a therapeutic plasma concentration for potent drugs and reduce the number of doses required. Another major benefit with such systems is in treatments demanding high dosages, where a sustained release spreads the drug subunits over time and, hence, drug release occurs over a large area avoiding local drug concentration close to the toxicity level. Controlled release refers to the release rate controlling system, including both sustained and delayed drug release.. 3.3.1 Tablets Controlled release systems are designed for all administration routes. One way to achieve a sustained drug release from a tablet is to form a binary system consisting of one insoluble polymer19 surrounding the finely dispersed drug which may be readily20-22 (Paper III and V) or sparingly23, 24 16.

(132) (Paper IV) soluble. The tablet does not disintegrate and thus serves as a ratecontrolling diffusion medium. Ethyl cellulose, which is a modified wood pulp cellulose by etherification is such an insoluble polymer.10 Being hydrophobic, it is mostly used as a coating material10 but also as a pharmaceutical excipient material in sustained release products. In a binary system the components are usually randomly mixed and the probability to find the drug/polymer at an arbitrary location in the matrix is thus equal to the volume fraction of the drug/polymer. The drug release process from such systems can be explained by percolation theory describing properties of clusters of randomly occupied sites.7, 21. 3.3.2 Gels Hydrogels are two-component semisolid systems rich in water, formed by polymers linked to an interlaced network, forming a mesh that holds the liquid phase. One of the characteristics of a hydrogel is the continuous structure providing solid-like properties. A commonly used hydrogel for pharmaceutical applications is Carbopol, which is used for several routes of drug administration.5 The drug molecules in such a gel are dispersed in the liquid phase and it is a major challenge to obtain sustained drug release from pharmaceutical gel systems. One approach is to use the knowledge of cationic systems. In a cationic system, mixtures of two oppositely charged surfactants form aggregates, such as vesicles and branched and elongated micelles. Structurally complex drug molecules have been shown to form such aggregates,25 which prevents the drug from fast diffusion (Paper II).. 3.4 Mesoporous Silica Ordered mesoporous silica is one of the most promising drug carrier materials for controlled drug release today. The discovery of the mesoporous silica material was made by Kresge and co-workers26 within the zeolite-research field about fifteen years ago. Zeolites are crystalline microporous materials which exist both in naturally and synthesized form, the pore sizes are about 5-12 Å and the large surface area provides a high cation exchange capacity. In a mesoporous silica structure the pore size is about 30-100 Å and, as opposed to the microporous silica, the silica-wall surrounding them is amorphous. One of the advantageous properties for the mesoporous materials is the large total surface area of about 700m2/g, which means that one gram has the same total surface area as three tennis courts. In comparison; the human lung 17.

(133) has a surface area of “only” 75-80 m2,27 whereas ordinary pharmaceutical MCC, has surface areas of ~1 m2/g. Therefore the mesoporous materials have a high capacity for loading of functional materials such as drugs in the internal pore system (Paper VII).28 The synthesis of mesoporous silica relies on surfactant micelles as templates for the assembly, where structure geometry and pore size can be determined by the choice and combination of surfactants as well as by the synthesis conditions. The mesoporous silica family named AMS-n (anionic templated mesoporous silicas) are based on interactions between the surfactants’ acidic moiety and anionic surfactants used as co-structure directing agents (Paper VI).29 Silica is a non-toxic, hard material. Different types of mesostructures can be designed and finally come out as either microspheres or monoliths, which might also be used as a bone tissue regenerator.30 Another major interesting property of mesoporous silica is the possibility of functionalizing the silica walls within the porous system.30. 18.

(134) 4. Transport processes. 4.1 Diffusion Diffusion refers to a thermally driven random motion of particles which tends to levelling out their concentration in a medium. In the study of drug release the diffusing entities are the drug molecules and the medium in which they diffuse is either the water filled pores in the drug delivery system (Paper I, IV, V, and VII) or equivalently the liquid phase in the gel system (Paper II). The driving force is concentration gradients and each entity moves by Brownian motion.18 The motion of diffusing molecules in a drug delivery matrix can be described by a random walk process. The first 60 % of the drug release process follows a general power-law equation,7, 31-33. Q. a bt k ,. (1). where Q is the amount of drug released per unit exposed area of the drug delivery system, a and b are constants, t is time and k is a transport coefficient. This equation is valid for drug release from both Euclidian and fractal (irregular but self similar) matrices. The transport coefficient characterizes the diffusion process which may be separated into three different cases according to the following:34-36 Case I corresponds to normal Fickian diffusion and matrix controlled release. Case I is obtained if there are no changes in the matrix structure as a result of interactions with the drug molecules. For planar systems, a typical square-root-of-time behaviour is observed, whereas geometry effects result in release exponents of 0.45 and 0.43 for cylindrical and spherical systems, respectively. Case II diffusion corresponds to zero order release kinetics with k = 1. Case II diffusion is obtained when there are strong drug–matrix interactions, mostly caused by swelling of the matrix, and the matrix relaxation rate is much slower than the diffusion rate. Case III diffusion, or anomalous diffusion, occurs when the matrix relaxation rate is on the same time scale as the diffusion rate. Depending on 19.

(135) whether diffusion is the slower or faster process it is called sub- (k<0.5) or super diffusion (0.5<k<1). Diffusion controlled release from a planar system may be described by the Higuchi square-root-of-time law;37. Q. DCs (2Cm I Cs )t .. (2). Here D is the effective diffusion coefficient of the drug inside the matrix, and Cm is the total amount of drug present in the matrix per unit volume, I is the total porosity of the matrix, defined as the volume fraction of pores when the drug material has been removed, and Cs is solubility of the drug in the release medium. For the equation to be valid Cm must be larger than ICs in order to reach a pseudosteady-state (PSS) condition during the release process, i.e., a sufficiently slow movement of the boundary between the region containing solid and only dissolved drug. Although Eq.(2) originally was derived for a planar geometry, it correctly predicts the initial slope in a Q vs. t plot, used for the extraction of D , also for other geometries (see Paper V and references therein).. 4.2 Conduction In an electric field the motion of charges is referred to as migration. The fundamental measurement to study the ionic motion is that of electrical resistance, which inverse is defined as the conductance, G. The conductance is related to the conductivity, V, as, G V. A , l. (3). where l is the conduction distance and A the cross sectional area of the conduction path. In the following equations, we have for simplicity assumed that only one type of charged species contributes to the conduction. The density of charge carriers (ions), n, is related to the conductivity via their mobility, ȝ, and their charge, q, as,. V. nqµ .. (4). The mobility is defined as the ionic drift speed in an applied field, of 1V/m, and accordingly the unit is m2/sV. Ionic interactions affect the drift speed and are taken into account by the corrections from increased concentration 20.

(136) by the Kolraush law38 and from increased temperature by the Arrhenius law;18 In a strong electrolyte the mobility varies with ionic density according to Kolrausch law38 1. µ n

(137) µ 0 Bn 2 ,. (5). where µ 0 is the average mobility at infinite dilution and B is a constant. The Arrhenius law describes the temperature dependence of many kinetic processes in nature including ionic mobility, hence,. µ T

(138). µ0 e. EA kBT. ,. (6). where ȝ0 is the mobility in at a certain reference temperature, kBT the thermal energy.and EA the activation energy.. 4.2.1 Einstein relation Fickian diffusion is governed by a concentration gradient whereas migration is governed by an electric potential gradient, i.e., and electric field. The mobility of ionic migration in an applied electrical filed can be related to the diffusion of the same type of ionic species in the absence of an electric field through the Einstein relation,18 D. P k BT q. .. (7). 4.3 Percolation A two component system of which one part diffuses through the other, can be described by percolation theory.7, 21, 39 Two percolation thresholds exist, one for each component at the volume fraction where it begins to span the entire matrix. When the amount of drug in a drug-polymer system is lower than the drug percolation threshold, only the polymer component spans the whole tablet while the drug is (partly) trapped within the matrix structure. Analogously, when the amount of polymer is lower than the polymer percolation threshold, only the drug component spans the tablet, which means that the matrix will collapse into separate fragments upon drug release. 21.

(139) For intermediate amounts of drug or polymer, both components span the matrix. Also when the porosity is nonzero, it is usually possible to retain this simple two-component description, provided the solid drug and the empty pore space between them are considered to constitute a single non-polymer component. Its volume fraction may be called the total matrix porosity, defined as the porosity of the empty, i.e., fully extracted, matrix (see Paper III and references therein). Once water has dissolved the drug, drug release occurs by diffusion. Immediately above the percolation threshold, Ic, the effective diffusion coefficient is expected to follow a scaling law that is insensitive to network structures and microscopic details, of the form 35 D. s. F D0 I Ic

(140) ,. (8). where ȤD0 is a scaling factor and s is a transport exponent, also called the conductivity exponent. The conductivity exponent depends on the geometry of the system and equals 2 for a three dimensional structure in the vicinity of the percolation threshold.35 An analogous equation describes ionic conductivity percolation, with the dc part of the conductivity substituted for the effective diffusion coefficient; s. V dc I

(141) V 0 I Ic

(142) .. (9). Here V0 is a constant, dependent on Ic but not on I, proportional to the conductivity of the component material with the highest conductivity (Paper III and V).. 22.

(143) 5. Materials and Sample Preparation. Four different types of materials were analysed: 1) MCC and 2) ethyl cellulose, the most common drug matrix materials used today, both in tabletted form, 3) a carbopol gel, a common pharmaceutical material used as drug vehicle in transdermal systems, and finally 4) well-defined mesoporous structured silica particles, potential future drug exipient materials.. 5.1 Tablets 5.1.1 Excipient material Microcrystalline cellulose (MCC; Avicel PH 101, Lot 6536, FMC, USA) Ethyl cellulose (EC, Sigma-Aldrich Chemie GmbH, Germany; apparent density 1.14 g/cm3 and viscosity 10 mPas). 5.1.2 Model drugs Sodium Chloride (NaCl; Merck, Germany; apparent density 2.17 g/cm3 and solubility 360 mg/ml) Acetylsalicylic acid (ASA; Sigma-Aldrich Chemie GmbH, Germany; apparent density 1.35 g/cm3 and solubility 3.3 mg/ml). 23.

(144) 5.1.3 Sample preparation MCC/NaCl tablets (Paper I) For tablet manufacturing, flowability is an important parameter in the compaction process. The untreated threadlike fibres of MCC were therefore first ground into powdered cellulose and then diluted in water (together with the drug: 30% NaCl and 70% MCC) and spray dried into agglomerated microcrystalline cellulose (AMC) that are hollow shaped, spherical particles. The size of the particles was determined by the feeding rate and temperature of the air flow during the drying process. Because of the good flowability no lubrication or other additional components were necessary for compaction of the tablets. Tablets were made at the three compaction pressures 50, 100, and 200 MPa, The powder was kept at 45-50% relative humidity both before and after compaction of tablets. EC/NaCl Tablets (Paper III, V) EC and NaCl was sieved into desired size fractions; 180-250 ȝm for NaCl and 224-312 ȝm for EC, selected because they result in particles of approximately the same weight, thus ensuring a good mixing homogeneity. The components were then mixed into nine fractions and dry mixed, before storing at 45-50 % relative humidity. The powder was carefully weighed to result in equally sized tablets,compacted at 400 MPa, and stored at 45-50 % relative humidity. The NaCl content ranged from 10 to 90 wt %, corresponding to a NaCl volume fraction T between 0.05 and 0.75. These tablets are henceforth referred to as NaCl10 to NaCl90 tablets. EC/ASA Tablets (Paper IV) The same procedure as for the EC+NaCl tablets was used. The size fractions were selected to 180–212 ȝm for ASA and 125–180 ȝm for EC. Powder mixtures of 30% ASA and 70% EC were compacted at 100 MPa into two different tablet heights of approximately 1.8 and 3.6 mm.. 24.

(145) 5.2 Gels 5.2.1 Polymer Carbopol 940 NF (C940; was a gift from BF Goodrich, Brecksville, OH). 5.2.2 Drug Diphenhydramine (DH; Sigma-Aldrich Sweden AB, Stockholm, Sweden) is an antihistamine. The drug molecule has a complex structure with a charged head group. Sodium dodecyl sulfate (SDS; Sigma-Aldrich Sweden AB, Stockholm, Sweden) is a cationic surfactant.. 5.2.3 Sample preparation The Carbopol gels under study in Paper II, were prepared in the following manner: 2% Carbopol gels were made by dispersing the polymer powder in 0.9% NaCl solutions. The dispersions were stirred at room temperature for approximately 1 h, using magnetic stirring rods, whereupon NaOH was added to neutralize the samples to approximately pH 7. Drug and drug/surfactant solutions, of 0.9% NaCl, were added to the polymer dispersions at a 1:1 ratio, ending up with a 1% Carbopol gel with either the drug mono dispersed in the matrix or as aggregates of drug and surfactant in micellar formation, see figure 2. The pH was finally adjusted to 7.3-7.5, using NaOH.. 25.

(146) Figure.2 Cryo-TEM picture to the left showing the gel that has freely dispersed drug molecules, i.e. diphene hydramine in, the gel. The right picture shows the gel that has ring-formed vesicles. Vesicles are formed of diphene hydramine together with surfactant molecules, SDS. The bar indicates 200 nm.. Concentration data for the gel type containing freely dispersed drug molecules (A) and for the vesicle forming gel structure (B) are summarized in table 1. Table 1. Total concentration, n of each component in the two gels under study C940. diphenhydramine. Gel A. 1%. 14 mM. Gel B. 1%. 14 mM +. Na+ and Cl- ions*. SDS. 440 mM 26 mM. 466 mM -. *Concentration of Na ions plus the concentration of Cl ions.. 26.

(147) 5.3 AMS-n, mesoporous silica 5.3.1 Material Surfactants are amphiphilic molecules that contain a charged head group and an uncharged tail. They are often used to change the surface property of a material or a compound. In a solution above the critical micelle concentration the surfactants form micelles of different sizes and properties, and below a certain temperature (Krafft temperature) the surfactants form viscous gels. 3-aminopropyl triethoxy silane (APES; Sigma-Aldrich Sweden AB, Stockholm, Sweden) is an anionic co-structure directing agent (CSDA) which has a charged amine group. Tetraethyl orthosilicate (TEOS; Sigma-Aldrich Sweden AB, Stockholm, Sweden) is used in the synthesis process as the silica source.. 5.3.2 Model Drugs The surfactants studied as model drugs were: N-Lauroyl-L-glutamic acid (C12GlutA; Sigma-Aldrich Sweden AB, Stockholm, Sweden) N -Lauroyl-L-alanine (C12Ala; Nanologica AB, Uppsala, Sweden).. In a neutral solution C12GlutA has two negative charges on the head group and C12Ala has one.. 5.3.3 Synthesis In a typical experiment the surfactant is dissolved at temperatures between room temperature and 80 qC, in distilled water. After complete dissolution of the surfactant the CSDA, APES, is added under stirring at the synthesis temperature followed by the addition of the silica source, TEOS, after a period of time, t, where t may vary according to the desired AMS-n mesostructure.40, 41 The synthesis gels are maintained at the synthesis temperature for a period of ~1 day, before transferring them to an oven at 100 °C for a further 2 days. The solid samples are then filtered, and dried overnight at RT, under 27.

(148) the flow of air. Figure 3 shows typical mesoporous silica nano particles, with the regularity of the system seen in the inset (Paper VI and VII).. Figure 3. SEM picture of typical mesoporous silica particles. A TEM image is shown in the inset.. 28.

(149) 6. Experimental Methods. 6.1 Electrodynamic methods Electrodynamic methods assess the motion of charged bodies, ions, or rotating dipoles in response to an electromagnetic field and offer insight into the nanoscale properties of materials.42 The ionic motions in the presented work were monitored by three different electrodynamic methods: A constant potential was applied across the studied sample and the current response was monitored as a function of time (Transient Ionic Current measurements, Paper II). A sinusoidal potential with varying frequency was applied across the sample and the current response was monitored as a function of frequency (Dielectric spectroscopy, Paper II and III). A sinusoidal potential with constant frequency was applied and the current response was monitored as a function of time (Alternating Ionic Current measurements, Paper I, IV, V, VI and VII).. 6.1.1 Alternating Ionic Current (AIC) measurements The AIC technique is used to study the drug release in situ.16 The AIC experimental set-up consists of a function generator, two multimeters, an external reference resistance and a sample cell, in which the drug delivery system is placed. The sample cell is a liquid filled container with two electrodes mounted on two opposite sides (figure 4). The method allows for detection of release process of drugs that ionize upon dissolution.. 29.

(150) Figure 4. AIC sample cell, here placed in an oven, in preparation for a stable temperature run above room temperature.. An alternating voltage is applied across the sample cell (with a frequency of 10 kHz) in order to avoid electrode polarization. During drug release, the number of charged drug entities in the dissolution medium increases and the cell conductance, G, is recorded as a function of time, t. From cell geometry and liquid amount, i.e., cell length, l and cross sectional area of liquid, A, the conductivity is determined by Eqs. (3) and (4). The mobility can be determined from a plot of the conductivity versus ion density, Eq. (4). When more than one type of ionic species is present (which usually is the case) this procedure yields a value for the average ionic mobility.. 6.1.2 Dielectric Spectroscopy Dielectric spectroscopy is an electrodynamic method that determines the frequency-dependent conduction properties of a sample. A sinusoidal voltage is applied across the sample situated between two electrodes, see figure 5, resulting in a current response governed by movements of charge carriers present in the sample.. 30.

(151) Figure 5.Dielectric measurement cell, equipped with exchangeable electrode plates, a moveable stage, by a micrometer screw, to adjust and measure electrode spacing, and a Teflon guard ring to avoid stray-field contributions.. The frequency of the voltage is scanned from a maximum to a minimum value. The measured current response can be interpreted in terms of several complex frequency dependent quantities such as impedance, Z*, conductivity, V*, and dielectric permittivity, İ*. The real part, V ' , of the conductivity is related to the imaginary part, H '' , of the dielectric permittivity as. ı'. Ȧİ0 İ '' ,. (10). where Z is the angular frequency and İ0 is the permittivity of free space (8.854×10-14 F/cm). At high frequencies, the movable ions in a sample will only have time to move a very short distance before the direction of the applied sinusoidal field is reversed and the ions are forced to change their direction of motion. Thus, at high enough frequencies, the ions will be able to move unhindered by blocking material structures or electrodes as if they were free. The conductivity associated with this motion can be expressed as in Eq. (4), with the ion mobility related to the diffusion coefficient D according to Eq. (7).. 31.

(152) At lower frequencies, when ions are blocked either by obstacles microscopically inherent in the materials structure or by the external electrodes, the distance d between the blocking features can be related to the ion diffusion coefficient and the angular frequency Z0, signifying the lower limit of the frequency region for unhindered motion, according to Dı hf. d. İ0 İ'hf. . 1. .. Ȧ0. (11). Here İ'hf denotes the real part of the relative dielectric permittivity in the frequency region for unhindered ionic motion, i.e., where V ' V hf . The above equation is obtained by equating the imaginary part of the relative dielectric permittivity in the high frequency region,. H ''hf. V hf , ZH 0. (12). with the imaginary part of the ion-blocking low-frequency relative permittivity43. H ''lf. ZH 'hf d 2 D. ,. (13). at the angular frequency Z=Z0. 6.1.2.1 Power-law method. In a binary system of one conducting and one insulating component the frequency dependent conductivity is not negligible over the entire frequency region. Extraction of the dc conductivity in materials with high dielectric loss can be done according to the power-law method.44 The real part of the conductivity of an ion conducting material may be expressed as. V ' Z

(153) V dcion V ac Z

(154) ,. (14). where V dcion is the ionic conductivity of the material, related to the ionic charge, the ionic concentration and mobility through Eq. (4). The frequency dependent ac component V ac (Z ) of the conductivity may originate from dipolar relaxations and charge transport processes not linked to the ionic transport or from other processes related to the ionic motion like electrode polarizations. These processes increase the dielectric loss of the material and their. 32.

(155) contribution should not be included in the conductivity extracted for analysis of long-range ion transport percolation. In order to obtain correct data for a percolation study, the lack of a perfect plateau in V '(Z ) must be taken into consideration. This can be done by extracting V dcions from V '(Z ) according to the power-law method developed in Ref. 44. The method is based on the assumption that the ac part of the conductivity in Eq. (14) can be expressed as an approximate power-law within some frequency range, V ac (Z ) v Z m , where m is a constant, see figure 6a. By differentiation of Eq. (14) with respect to ln Ȧ it is found that § 1 · § dV '(Z ) · ¸¨ ¸, © m ¹ © d ln Z ¹. V '(Z ) V dcion ¨. (15). and V dcion can thus be extracted from a linear fit of V ' Z

(156) vs dV '(Z ) d ln Z , see figure 6b.. Figure 6a. The conductivity V '(Z ) and its derivative, dV '(Z ) d ln Z vs. frequency for a 60 wt% NaCl tablet. The frequency region for which the linear extraction ion of V dc should be performed according to the power-law method is marked with a square.. 33.

(157) ion Figure 6b. Extraction of V dc from linear fit of V ' (Z ) vs. dV '(Z ) d ln Z from the frequency region indicated by the square in panel a.. 6.1.3 Transient Ionic Currents measurements The sample/electrode configuration in transient current measurements is the same as that for dielectric spectroscopy. Instead of a sinusoidal frequency dependent voltage, however, a constant voltage step is applied across the sample and the resulting current is measured as a function of time. The potential across the sample is changed from zero to a specified value by taking the sample from a uniform charge distribution to a polarized state. Neglecting space-charge effects and assuming that the initial current decay is dominated by migration of ions toward an ion blocking contact, both n and l can be obtained by fitting the measured current response to45, 46. I (t ). 34. AV dcU § µU · exp ¨ 2 t ¸ . d © d ¹. (16).

(158) Here A is the electrode area, U is the applied potential, and V dc is the dc conductivity of the ions. The ion concentration n contributing to the current response can be extracted from V dc using Eq. (4). The above equation holds when there are only identical ions present. The equation is, however, easily adapted to the case when more than one type of ions reside in the sample simultaneously by just adding one additional term-identical to the one already at the right-hand side of the equation-per ion type.46. 6.2 Pore structure determining methods Porosity is defined as the ratio of the void volume to the total volume of the material, mostly given as a percentage. Almost all solid materials are porous in some sense. Dullien47 states that either “the material must contain voids, free of solids, embedded in the solid or semisolid matrix” or “it must be permeable to a variety of fluids” to qualify as porous. In a perfect crystalline material, the atoms are situated close to one another in an ordered structure. Only smaller atoms can migrate through such a material but in most materials mismatches exist, creating holes and pathways for other, larger atoms to migrate through. On the shortest length scale the materials are not considered to be “porous”, but rather permeable, with the unit mol/(m×s×Pa) for the permeability. Taking one step up on the length scale, the particles formed by molecules are considered. The space inside and between particles contributes to the intra-particular and inter-particular porosity, respectively. The density of a material can be interpreted in two ways, both involving the material porosity. The simplest way to calculate the density is to divide the material mass with the total material volume; the density is then called the bulk density. Another way to calculate the density is to disregard the volume of space in the material and only measure the volume of solid material, the density is then regarded as the true density. The latter measurement is normally made by pycnometry, using air or helium that can intrude into all cavities of the material to determine the true volume. However, since inaccessible pores may exist in the material, the obtained density is often referred to as the apparent density. For (pharmaceutical) materials the two most commonly used methods to measure porosity are gas adsorption and mercury intrusion. For small pores in the size range of 0.3-300 nm gas adsorption is used and for larger pores in the size range of 3 nm-200 ȝm mercury intrusion is preferred.. 35.

(159) 6.2.1 Gas adsorption With gas adsorption techniques, the surface area of a material and the pore structure can be extracted from the number of molecules that are adsorbed in the structure by analysing the gas adsorption isotherm, i.e., the number of adsorbed molecules plotted vs. the relative gas-pressure when the recordings are made at constant temperature, T. The dry sample is first degassed to get an as clean surface as possible and then cooled in liquid N2 to 77K. At this temperature inert gases such as nitrogen, argon and krypton will adsorb to the surface. The interaction between gas (adsorbate) and surface (adsorbent) is associated with van der Waals type interactions and is regarded to be reversible. The choice of adsorbate mainly depends on the sample. Nitrogen is the most commonly used adsorbate for examining pharmaceutical material, but if the surface area is very low, argon or krypton may be used as both give a more sensitive measurement, because of their lower saturation vapor pressures at liquid nitrogen temperature.48 6.2.1.1 BET. Starting the adsorption process at low pressure a monolayer of adsorbate is formed. In the relative pressure region below 0.35 the monolayer is completed and a multilayer is starting to build up (figure 7). The total surface area can be determined by the BET equation49. p V ( p0 p). 1 (C 1) p , Vm C Vm C p0. (17). where V is the volume adsorbed at pressure p and p0 the vapour pressure of the same gas at the same temperature, Vm is the volume of gas adsorbed when the entire adsorbent surface is covered with a monolayer and C is a constant only dependent on enthalpy (heat) of adsorption in the first layer.. 36.

(160) Figure 7. A type II adsorption isotherm showing unrestricted monolayer-multilayer adsorption on MCC tablets. One monolayer is assumed to be completed in the first knee which sets the upper limit for the region from which the BET surface area is determined.. 6.2.1.2 BJH. By taking into account both multilayer gas adsorption and capillary condensation in cylindrical pores Barret, Joyner and Halenda,50 referred to as BJH, showed how the pore-size distribution of a porous medium could be obtained from gas adsorption isotherms (or more correctly from desorption isotherms). The pore-size distribution is determined at higher pressures beyond monolayer coverage. The pores are filled with condensed gas and their size, r, are related to the relative pressure according to the Kelvin equation51. ln. p p0. . 2J VL cos D , rRT. (18). where J is the surface tension of the liquid (adsorbed atoms or molecules), VL the molar volume of the liquid, D the contact angle between the surface and the liquid, R the gas constant and T the absolute temperature. Pores in the range from 0.3-200 nm can be determined by this method. 37.

(161) 6.2.2 Hg-porosimetry Mercury is a non-wetting fluid, which means that the contact angel in the interface to a solid material is high (>90q), and is therefore not able to enter a capillary without an applied force. The method of mercury porosimetry, developed by Ritter and Drake52 records the applied force that is needed to force a certain volume of Hg into the porous material. The analysis of pressure versus intruded mercury volume (p-V) is the most direct way to analyse the pore structure of a material. Pores in the size range 3 nm-200 ȝm can be determined by this method. Washburn53 derived a model, assuming cylindrical pores, relating the applied pressure, p and the pore radius, r as p. 2J cos D , r. (19). where Ȗ is the surface tension of mercury and Į the contact angle between mercury and the sample. Starting the measurement at the lowest pressure the largest pores will be filled first, increasing pressure makes smaller pores accessible to mercury. Using the Washburn equation the pore radius and surface area can be calculated. The major drawback of the calculation is that it assumes only cylindrical pore shape, which is seldom the case. Void sizes are therefore always underestimated in structures where smaller pores are entrances to voids, resulting in estimated void diameters in the interval between that of the “throat” of the void and that of the actual void body.35 Pore volume distribution, Dv(d), is related to the pore diameter, d, according to 52 Dv (d ). p dV . d dp. (20). The total pore volume is the total intruded volume of mercury at the highest pressure determined. An extrusion curve can be determined as the pressure is decreased and mercury leaves the pores. It may differ, though, from the intrusion curve since mercury often gets trapped inside the pore structure. Under the assumption that the contact angle is constant, the hysteresis between intrusion and extrusion curves gives information about the ability to trap mercury in cavities and thus about the complex pore shape.54. 38.

(162) 7. Results and Discussion. 7.1 Drug diffusion in MCC tablets Drug release measurements at different temperatures were performed to extract information about the drug release process by analyzing the environment and speed of the drug diffusion within the delivery vehicle (Paper I). Tablets formed from AMC containing NaCl as a model drug were used for this purpose.. 7.1.1 Tablet characterization The BET analysis of the N2 adsorption isotherms showed that the total surface area of the tablets decreased from a value of 1.06 m2/g for the tablets compacted at 50 MPa to only 0.75 m2/g for those made at 200 MPa. Consistently, the BJH analysis showed on a decrease in pore volume of pores having a diameter between 17 and 3000 Å from 4.0 mm3/g to 2.5 mm3/g. Although an increased densification of the particles occurred from increasing compaction pressure, the spherical AMC particle shape was preserved (figure 8) in all tablets with a particle radius of about 10 ȝm.. 39.

(163) Figure 8. SEM pictures of uncompressed AMC powder (a) and of tablets compressed at 50 (b), 100 (c) and 200 MPa (d).. 7.1.2 Drug release Release measurements, using the AIC method described above was conducted at seven different temperatures (6, 23, 33, 43, 50, 55, and 63qC). The release was completed within 2 hours for all temperatures. In the release rates, though, no significant difference between the tablets compacted at different pressures was obtained. This finding suggests that the AMC granules in contact with water swell to a size and shape that is only slightly affected by their compaction history.. 40.

(164) Figure 9. Effective diffusion coefficients for Na+ and Cl- in MCC tablet granules vs. inverse thermal energy calculated for the compaction pressures 50, 100, and 200 MPa. Note that the diffusion coefficients have been normalized by their values at room temperature.. 41.

(165) The effective diffusion coefficients are thermally activated, with activation energies of the order of 0.15 to 0.17 eV (figure 9), which is almost identical to that obtained for the average ionic mobility in pure water. Since the diffusion coefficient is proportional to the mobility, according to the Einstein relation, Eq. (7), this finding strongly points towards the fact that diffusion occurs in liquid filled pores inside the AMC granules. If the AMC would have constituted a separate phase, through which diffusion occurred, the activation energy had, most likely, been different. Even though this conclusion, as such, not is unexpected it, nevertheless, shows how temperaturedependent release measurements successfully may be utilized to elucidate important aspects of the drug release process. Having established that the drug release process in the AMC granules most likely takes place within liquid-filled pores, we were able to use Eq.(2) to get an absolute estimate of the diffusion coefficient. The effective diffusion coefficient of Na+ and Clwithin the AMC granules was found to be ~ 7.5 × 10-10 cm2/s, which is ~ 4 orders of magnitude lower than for unhindered diffusion of Na+ and Cl- in water but similar to the diffusion coefficient for protons and OH- ions within MCC. This shows that drug and water transport inside delivery vehicles are intimately connected, and it therefore elucidates the necessity to understand the water transport properties of excipient materials to be able to tailor the drug release process from pharmaceutical tablets. For small drug ions such as Na+ and Cl-, it may very well be the interactions between the free hydroxyl groups of the cellulose with the water molecules in the hydration shell surrounding the drug ions that totally dominate the speed by which the ions are able to leave the cellulose tablet.. 7.2 Diffusion in EC tablets 7.2.1 Model calculations Drug release from matrix systems of cylindrical shape was analyzed in detail by using the finite element method in Paper IV. The model used combines the Noyes–Whitney and diffusion equations, and thus takes the effects of a finite dissolution rate into account. Model calculations showed that a finite dissolution rate may affect the release profile significantly, producing an initial delay. The equivalence between anisotropic release and isotropic release from a matrix with different dimensions was demonstrated. The predictions of the recently proposed PSS analysis of Zhou et al.55 were compared to the numerical results, and important discrepancies were found to exist. These were attributed to the simplifying assumption made in the PSS analysis that the region containing solid drug remains cylindrical in shape 42.

(166) throughout the release process. The proposed model was shown to describe experimental release data well for a drug releasing system consisting of the sparingly soluble model drug, ASA, incorporated in an inert EC matrix, figure 10.. Figure 10. Comparison between experimental (symbols) and theoretical (lines) fractions of released drug. The error bars indicate the standard deviations for three repeated measurements.. 7.2.2 Drug release Tablets formed from binary mixtures of EC and NaCl were examined. Drug release measurements were performed in 25 ml of distilled water as dissolution medium by the AIC method (Paper V). Figure 11 displays typical release profiles from nine different volume fractions for the first 5 hours.. 43.

(167) Figure 11 Amount of drug released per unit exposed tablet area for all tablet types under study.. Data corresponding to a fractional release between 5% and 60% was used to determine the release exponent using Eq. (1). Since EC does not swell in contact with water, it may be assumed that diffusion is purely matrix controlled (Case I diffusion) for release exponents close to 0.45 (cylindrical geometry). The release exponents closest to this value, i.e., k = 0.45±0.03, were obtained for the NaCl30, NaCl40 and NaCl50 tablets. Larger release exponents were obtained for tablets containing more than 50% (wt/wt) NaCl, whereas strong anomalous sub-diffusion was observed for the release from the NaCl10 and NaCl20 tablets.. 44.

(168) Figure 12. The effective diffusion calculated for different compositions by the Higuchi model for drug release.. From fittings of the Higuchi equation (2) to the nine release profiles, the effective diffusion coefficients were extracted and fitted to the scaling-law [Eq. (8)] of percolation theory, figure 12. From this fit the porosity percolation threshold could be determined as a 0.22.. 7.2.3 Dielectric spectroscopy In a frequency spectrum of a dry binary NaCl/EC system (Paper III) the conductivity decreases with decreasing NaCl content, see figure 13. Although a clear plateau is not visible for any composition, the dc conductivity region is more pronounced at high NaCl contents. The contribution from other processes becomes progressively more dominant as the NaCl content is lowered and the dc conductivity region is shifted towards lower frequencies. 45.

(169) Figure 13. Real part of the conductivity for the different tablet compositions.. In order to obtain correct data for the dc conductivity the power-law method was applied and the resulting V dcions were fitted to Eq. (9) according to percolation theory for both low and high I values. The low I region fit shows that the conduction path through the non-EC phase can be associated with a percolation exponent, s, of 2 and a percolation threshold, Ic, of 0.16. For tablet porosity larger than ~ 0.4 the conductivity is very well described by the effective medium theory (EMT) exponent s = 1 as seen in figure 14. The percolation exponent is in exact correspondence with the theoretically predicted value for a 3D conducting network.35. 46.

(170) Figure 14. The conductivity curve depicted by filled squares is obtained by employing the power-law method. Curve fits to the equations signifying percolation and effective medium theory are also included.. However, the percolation threshold of 0.16, which corresponds to a NaCl volume fraction of only ~ 0.06, is lower than values usually presented for percolating binary microgranular conduction systems. Brick-layer type (BLT) percolation models have previously been shown to predict percolation thresholds as low as Ic= 0.097 if corner sharing grains (third nearest neighbours) are assumed to be part of a conduction path. And in experiments, percolation thresholds as low as ~ 0.027 were found for nanogranular systems. A BLT model, allowing for so-called “nanometer-passageway diffusion” in short open channels between insulating grains, was employed to describe the low Ic values (see paper III and references therein). From figure 15 and figure 16a, below, showing Hg porosimetry and SEM data on the NaCl-EC systems, it is evident that pores of ~ 1ȝm width are present in the EC structure. (Note that the large pores of ~ 100ȝm widht, seen in figure 15, 47.

(171) stems from the underestimated void size after leaked-out NaCl grains). From figure 16b it is also clear that the separation between individual ~ 200ȝm sized NaCl grains is too large for a corner sharing BLT model to fully account for the low percolation threshold. With a monolayer of water present on the surface of the pores it was possible for us to conclude that the low percolation threshold value could be explained by the occurrence of waterlayer-assisted ion conduction in ȝm-sized channels between cubic NaCl grains in the EC matrix (Paper III).. Figure 15. Differential pore volume, dV/dlog(d), vs. pore diameter, d, as obtained from Hg porosimetry measurements on the EC matrix after the NaCl had been allowed to leak out from 20, 50 and 80 wt% NaCl containing tablets.. 48.

(172) Figure 16 a) NaCl80 as-compacted showing cavities about 1ȝm in size. b) NaCl20 leaked out showing that the separation between individual ~ 200ȝm sized NaCl grains is too large for a corner sharing BLT model to fully account for the low percolation threshold.. A comparison of the results from AIC (Ic=0.22) and dielectric spectroscopy (Ic=0.16) concludes that the probing mechanisms differ (paper V): In the AIC measurements the ions had the possibility to escape the tablet matrix in all directions whereas in the dielectric spectroscopy measurements only ion movements in the direction towards the two planar surfaces could be probed, figure 17.. Figure 17. Illustration of ion transport assessment in the AIC measurements (left) and in dielectric spectroscopy (right).. Considering this fact, one would expect to find a lower percolation threshold from the AIC study than for the dielectric spectroscopy measurements. However, the fact that a higher threshold value was obtained from the former, could be explained by the differences in probing mechanisms: In the AIC method only the Na+ and Cl- ions located in pores that were in direct contact with the surrounding water were probed, whereas in dielectric spectroscopy, the conductivity of the moving ions was extracted from an ac frequency interval slightly above the frequency region where the ions were blocked, figure 13, either at the electrodes or at the end of closed channels 49.

(173) long enough to let the ions move freely at the frequencies in the probing interval. In addition to the ions situated in pores that were in contact with the electrodes at the outer planar surfaces, this probing mechanism allowed for some contribution to the conductivity also from ions that moved through a substantial part of the tablet without reaching these outer surfaces. At porosities slightly below that required for the establishment of a continuous pore network that spans through the whole matrix, a network of longer pores with closed ends is being created. The lower percolation threshold detected by dielectric spectroscopy may represents the porosity for which such a closed network of longer pores is formed while the threshold found in the AIC release study signifies the porosity at which this pore network is opened and reaches the outer tablet surfaces. These results clearly indicate that for practical purposes, i.e., for the development of pharmaceutical dosage forms, percolation thresholds obtained from dielectric spectroscopy are under estimated and need to be corrected or reconsidered.. 7.3 Structural characterization of gels Dielectric spectroscopy and transient current measurements were used to obtain information about the concentration and motion of drug molecules inside the gel structure and, hence, to provide information about the surroundings of the different molecules (Paper II).. 7.3.1 Dielectric spectroscopy Dielectric response of both the A and B gels (table 1) was determined in the frequency range from 10-3 to 107 Hz, figure 18.. 50.

(174) Figure 18. Dielectric response of the diphenhydramine containing Carbopol gel (A gel) as well as of the diphenhydramine and SDS containing Carbopol gel (B gel) displayed as the real part, V ' , of the complex conductivity as a function of frequency.. The following analysis of the frequency spectrum was made from the high frequency towards the low frequency regions: 100-10 kHz: A more or less constant conductivity of ~16 mS/cm for both the A and B gels is seen in the high-frequency region. This plateau stems from the movement of the small Na+ and Cl- ions present in the gel.11, 56 The average diffusion coefficient for the Na+ and Cl- may be extracted using Eqs. (4) and (7). In both the A and B gels, the diffusion coefficient for Na+ and Cl- was about 50% lower than in free water18 which may partly be attributed to an increase in microviscosity.57 In addition, the polymer chains in the gel form a rather rigid structure causing the system to have an inhomogeneous charge distribution inducing interactions that may affect the ionic motions in the gel, and thus cause a lowering of diffusion coefficients. 10-2 kHz: The conductivity starts to decrease toward lower frequencies at ~10 kHz for the A gel and ~2 kHz for the B gel. To use Eq. (11) for calculating the distance over which the ions are moving before being blocked, one 51.

No results found